1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 340,925 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 340,915 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     62
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      1
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-09-16          East of England      0
## 201   2020-09-17          East of England      0
## 202   2020-09-18          East of England      0
## 203   2020-09-19          East of England      0
## 204   2020-09-20          East of England      2
## 205   2020-09-21          East of England      0
## 206   2020-09-22          East of England      2
## 207   2020-09-23          East of England      1
## 208   2020-09-24          East of England      0
## 209   2020-09-25          East of England      1
## 210   2020-09-26          East of England      1
## 211   2020-09-27          East of England      1
## 212   2020-09-28          East of England      2
## 213   2020-09-29          East of England      2
## 214   2020-09-30          East of England      2
## 215   2020-10-01          East of England      2
## 216   2020-10-02          East of England      1
## 217   2020-10-03          East of England      1
## 218   2020-10-04          East of England      0
## 219   2020-10-05          East of England      0
## 220   2020-10-06          East of England      4
## 221   2020-10-07          East of England      6
## 222   2020-10-08          East of England      3
## 223   2020-10-09          East of England      1
## 224   2020-10-10          East of England      6
## 225   2020-10-11          East of England      2
## 226   2020-10-12          East of England      2
## 227   2020-10-13          East of England      1
## 228   2020-10-14          East of England      3
## 229   2020-10-15          East of England      4
## 230   2020-10-16          East of England      5
## 231   2020-10-17          East of England      6
## 232   2020-10-18          East of England      7
## 233   2020-10-19          East of England      5
## 234   2020-10-20          East of England      9
## 235   2020-10-21          East of England      7
## 236   2020-10-22          East of England      7
## 237   2020-10-23          East of England     14
## 238   2020-10-24          East of England      1
## 239   2020-10-25          East of England     10
## 240   2020-10-26          East of England     10
## 241   2020-10-27          East of England      6
## 242   2020-10-28          East of England     12
## 243   2020-10-29          East of England     10
## 244   2020-10-30          East of England     12
## 245   2020-10-31          East of England     15
## 246   2020-11-01          East of England     14
## 247   2020-11-02          East of England      8
## 248   2020-11-03          East of England     14
## 249   2020-11-04          East of England     10
## 250   2020-11-05          East of England     10
## 251   2020-11-06          East of England     17
## 252   2020-11-07          East of England     10
## 253   2020-11-08          East of England     13
## 254   2020-11-09          East of England     13
## 255   2020-11-10          East of England     26
## 256   2020-11-11          East of England     14
## 257   2020-11-12          East of England     14
## 258   2020-11-13          East of England     21
## 259   2020-11-14          East of England     19
## 260   2020-11-15          East of England     13
## 261   2020-11-16          East of England     11
## 262   2020-11-17          East of England     17
## 263   2020-11-18          East of England     19
## 264   2020-11-19          East of England     23
## 265   2020-11-20          East of England     23
## 266   2020-11-21          East of England     16
## 267   2020-11-22          East of England     20
## 268   2020-11-23          East of England     17
## 269   2020-11-24          East of England     18
## 270   2020-11-25          East of England     15
## 271   2020-11-26          East of England     13
## 272   2020-11-27          East of England      2
## 273   2020-03-01                   London      0
## 274   2020-03-02                   London      0
## 275   2020-03-03                   London      0
## 276   2020-03-04                   London      0
## 277   2020-03-05                   London      0
## 278   2020-03-06                   London      1
## 279   2020-03-07                   London      0
## 280   2020-03-08                   London      0
## 281   2020-03-09                   London      1
## 282   2020-03-10                   London      0
## 283   2020-03-11                   London      5
## 284   2020-03-12                   London      6
## 285   2020-03-13                   London     10
## 286   2020-03-14                   London     13
## 287   2020-03-15                   London      9
## 288   2020-03-16                   London     15
## 289   2020-03-17                   London     23
## 290   2020-03-18                   London     28
## 291   2020-03-19                   London     25
## 292   2020-03-20                   London     44
## 293   2020-03-21                   London     49
## 294   2020-03-22                   London     54
## 295   2020-03-23                   London     63
## 296   2020-03-24                   London     86
## 297   2020-03-25                   London    112
## 298   2020-03-26                   London    129
## 299   2020-03-27                   London    130
## 300   2020-03-28                   London    123
## 301   2020-03-29                   London    145
## 302   2020-03-30                   London    151
## 303   2020-03-31                   London    183
## 304   2020-04-01                   London    202
## 305   2020-04-02                   London    191
## 306   2020-04-03                   London    199
## 307   2020-04-04                   London    231
## 308   2020-04-05                   London    195
## 309   2020-04-06                   London    198
## 310   2020-04-07                   London    220
## 311   2020-04-08                   London    239
## 312   2020-04-09                   London    207
## 313   2020-04-10                   London    171
## 314   2020-04-11                   London    178
## 315   2020-04-12                   London    159
## 316   2020-04-13                   London    166
## 317   2020-04-14                   London    143
## 318   2020-04-15                   London    143
## 319   2020-04-16                   London    140
## 320   2020-04-17                   London    101
## 321   2020-04-18                   London    101
## 322   2020-04-19                   London    103
## 323   2020-04-20                   London     96
## 324   2020-04-21                   London     96
## 325   2020-04-22                   London    109
## 326   2020-04-23                   London     77
## 327   2020-04-24                   London     71
## 328   2020-04-25                   London     58
## 329   2020-04-26                   London     53
## 330   2020-04-27                   London     52
## 331   2020-04-28                   London     44
## 332   2020-04-29                   London     45
## 333   2020-04-30                   London     40
## 334   2020-05-01                   London     41
## 335   2020-05-02                   London     41
## 336   2020-05-03                   London     36
## 337   2020-05-04                   London     30
## 338   2020-05-05                   London     25
## 339   2020-05-06                   London     37
## 340   2020-05-07                   London     37
## 341   2020-05-08                   London     30
## 342   2020-05-09                   London     23
## 343   2020-05-10                   London     26
## 344   2020-05-11                   London     18
## 345   2020-05-12                   London     18
## 346   2020-05-13                   London     17
## 347   2020-05-14                   London     20
## 348   2020-05-15                   London     19
## 349   2020-05-16                   London     14
## 350   2020-05-17                   London     15
## 351   2020-05-18                   London     11
## 352   2020-05-19                   London     14
## 353   2020-05-20                   London     19
## 354   2020-05-21                   London     12
## 355   2020-05-22                   London     10
## 356   2020-05-23                   London      6
## 357   2020-05-24                   London      7
## 358   2020-05-25                   London      9
## 359   2020-05-26                   London     14
## 360   2020-05-27                   London      7
## 361   2020-05-28                   London      8
## 362   2020-05-29                   London      7
## 363   2020-05-30                   London     12
## 364   2020-05-31                   London      6
## 365   2020-06-01                   London     10
## 366   2020-06-02                   London      8
## 367   2020-06-03                   London      6
## 368   2020-06-04                   London      8
## 369   2020-06-05                   London      4
## 370   2020-06-06                   London      0
## 371   2020-06-07                   London      5
## 372   2020-06-08                   London      5
## 373   2020-06-09                   London      5
## 374   2020-06-10                   London      8
## 375   2020-06-11                   London      5
## 376   2020-06-12                   London      3
## 377   2020-06-13                   London      3
## 378   2020-06-14                   London      3
## 379   2020-06-15                   London      1
## 380   2020-06-16                   London      2
## 381   2020-06-17                   London      1
## 382   2020-06-18                   London      2
## 383   2020-06-19                   London      5
## 384   2020-06-20                   London      3
## 385   2020-06-21                   London      4
## 386   2020-06-22                   London      2
## 387   2020-06-23                   London      1
## 388   2020-06-24                   London      4
## 389   2020-06-25                   London      3
## 390   2020-06-26                   London      2
## 391   2020-06-27                   London      1
## 392   2020-06-28                   London      2
## 393   2020-06-29                   London      2
## 394   2020-06-30                   London      1
## 395   2020-07-01                   London      3
## 396   2020-07-02                   London      2
## 397   2020-07-03                   London      2
## 398   2020-07-04                   London      1
## 399   2020-07-05                   London      3
## 400   2020-07-06                   London      2
## 401   2020-07-07                   London      1
## 402   2020-07-08                   London      3
## 403   2020-07-09                   London      4
## 404   2020-07-10                   London      0
## 405   2020-07-11                   London      1
## 406   2020-07-12                   London      1
## 407   2020-07-13                   London      1
## 408   2020-07-14                   London      0
## 409   2020-07-15                   London      2
## 410   2020-07-16                   London      0
## 411   2020-07-17                   London      0
## 412   2020-07-18                   London      2
## 413   2020-07-19                   London      0
## 414   2020-07-20                   London      0
## 415   2020-07-21                   London      1
## 416   2020-07-22                   London      0
## 417   2020-07-23                   London      2
## 418   2020-07-24                   London      0
## 419   2020-07-25                   London      1
## 420   2020-07-26                   London      0
## 421   2020-07-27                   London      1
## 422   2020-07-28                   London      0
## 423   2020-07-29                   London      0
## 424   2020-07-30                   London      1
## 425   2020-07-31                   London      0
## 426   2020-08-01                   London      0
## 427   2020-08-02                   London      3
## 428   2020-08-03                   London      0
## 429   2020-08-04                   London      0
## 430   2020-08-05                   London      0
## 431   2020-08-06                   London      1
## 432   2020-08-07                   London      0
## 433   2020-08-08                   London      0
## 434   2020-08-09                   London      0
## 435   2020-08-10                   London      0
## 436   2020-08-11                   London      1
## 437   2020-08-12                   London      0
## 438   2020-08-13                   London      2
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## 1461  2020-06-09               South East     10
## 1462  2020-06-10               South East     11
## 1463  2020-06-11               South East      5
## 1464  2020-06-12               South East      6
## 1465  2020-06-13               South East      7
## 1466  2020-06-14               South East      7
## 1467  2020-06-15               South East      8
## 1468  2020-06-16               South East     14
## 1469  2020-06-17               South East      9
## 1470  2020-06-18               South East      4
## 1471  2020-06-19               South East      7
## 1472  2020-06-20               South East      5
## 1473  2020-06-21               South East      3
## 1474  2020-06-22               South East      2
## 1475  2020-06-23               South East      9
## 1476  2020-06-24               South East      7
## 1477  2020-06-25               South East      5
## 1478  2020-06-26               South East      8
## 1479  2020-06-27               South East      9
## 1480  2020-06-28               South East      6
## 1481  2020-06-29               South East      5
## 1482  2020-06-30               South East      5
## 1483  2020-07-01               South East      2
## 1484  2020-07-02               South East      8
## 1485  2020-07-03               South East      3
## 1486  2020-07-04               South East      6
## 1487  2020-07-05               South East      5
## 1488  2020-07-06               South East      4
## 1489  2020-07-07               South East      6
## 1490  2020-07-08               South East      3
## 1491  2020-07-09               South East      7
## 1492  2020-07-10               South East      3
## 1493  2020-07-11               South East      4
## 1494  2020-07-12               South East      4
## 1495  2020-07-13               South East      5
## 1496  2020-07-14               South East      5
## 1497  2020-07-15               South East      6
## 1498  2020-07-16               South East      3
## 1499  2020-07-17               South East      1
## 1500  2020-07-18               South East      5
## 1501  2020-07-19               South East      2
## 1502  2020-07-20               South East      6
## 1503  2020-07-21               South East      4
## 1504  2020-07-22               South East      2
## 1505  2020-07-23               South East      3
## 1506  2020-07-24               South East      1
## 1507  2020-07-25               South East      1
## 1508  2020-07-26               South East      3
## 1509  2020-07-27               South East      1
## 1510  2020-07-28               South East      3
## 1511  2020-07-29               South East      2
## 1512  2020-07-30               South East      3
## 1513  2020-07-31               South East      1
## 1514  2020-08-01               South East      2
## 1515  2020-08-02               South East      4
## 1516  2020-08-03               South East      0
## 1517  2020-08-04               South East      0
## 1518  2020-08-05               South East      0
## 1519  2020-08-06               South East      2
## 1520  2020-08-07               South East      0
## 1521  2020-08-08               South East      2
## 1522  2020-08-09               South East      0
## 1523  2020-08-10               South East      2
## 1524  2020-08-11               South East      1
## 1525  2020-08-12               South East      1
## 1526  2020-08-13               South East      0
## 1527  2020-08-14               South East      0
## 1528  2020-08-15               South East      2
## 1529  2020-08-16               South East      1
## 1530  2020-08-17               South East      0
## 1531  2020-08-18               South East      2
## 1532  2020-08-19               South East      1
## 1533  2020-08-20               South East      0
## 1534  2020-08-21               South East      0
## 1535  2020-08-22               South East      0
## 1536  2020-08-23               South East      1
## 1537  2020-08-24               South East      0
## 1538  2020-08-25               South East      1
## 1539  2020-08-26               South East      0
## 1540  2020-08-27               South East      1
## 1541  2020-08-28               South East      2
## 1542  2020-08-29               South East      1
## 1543  2020-08-30               South East      0
## 1544  2020-08-31               South East      2
## 1545  2020-09-01               South East      1
## 1546  2020-09-02               South East      1
## 1547  2020-09-03               South East      0
## 1548  2020-09-04               South East      1
## 1549  2020-09-05               South East      0
## 1550  2020-09-06               South East      1
## 1551  2020-09-07               South East      0
## 1552  2020-09-08               South East      0
## 1553  2020-09-09               South East      0
## 1554  2020-09-10               South East      1
## 1555  2020-09-11               South East      1
## 1556  2020-09-12               South East      0
## 1557  2020-09-13               South East      3
## 1558  2020-09-14               South East      1
## 1559  2020-09-15               South East      2
## 1560  2020-09-16               South East      2
## 1561  2020-09-17               South East      3
## 1562  2020-09-18               South East      1
## 1563  2020-09-19               South East      1
## 1564  2020-09-20               South East      0
## 1565  2020-09-21               South East      3
## 1566  2020-09-22               South East      0
## 1567  2020-09-23               South East      2
## 1568  2020-09-24               South East      0
## 1569  2020-09-25               South East      3
## 1570  2020-09-26               South East      2
## 1571  2020-09-27               South East      2
## 1572  2020-09-28               South East      6
## 1573  2020-09-29               South East      3
## 1574  2020-09-30               South East      4
## 1575  2020-10-01               South East      4
## 1576  2020-10-02               South East      2
## 1577  2020-10-03               South East      1
## 1578  2020-10-04               South East      1
## 1579  2020-10-05               South East      2
## 1580  2020-10-06               South East      1
## 1581  2020-10-07               South East      4
## 1582  2020-10-08               South East      1
## 1583  2020-10-09               South East      1
## 1584  2020-10-10               South East      3
## 1585  2020-10-11               South East      3
## 1586  2020-10-12               South East      4
## 1587  2020-10-13               South East      2
## 1588  2020-10-14               South East      2
## 1589  2020-10-15               South East      3
## 1590  2020-10-16               South East      2
## 1591  2020-10-17               South East      3
## 1592  2020-10-18               South East      4
## 1593  2020-10-19               South East      7
## 1594  2020-10-20               South East      8
## 1595  2020-10-21               South East      9
## 1596  2020-10-22               South East      5
## 1597  2020-10-23               South East      7
## 1598  2020-10-24               South East      5
## 1599  2020-10-25               South East      9
## 1600  2020-10-26               South East     13
## 1601  2020-10-27               South East     10
## 1602  2020-10-28               South East     10
## 1603  2020-10-29               South East      7
## 1604  2020-10-30               South East      6
## 1605  2020-10-31               South East     15
## 1606  2020-11-01               South East     18
## 1607  2020-11-02               South East     13
## 1608  2020-11-03               South East     16
## 1609  2020-11-04               South East     10
## 1610  2020-11-05               South East     10
## 1611  2020-11-06               South East     16
## 1612  2020-11-07               South East     17
## 1613  2020-11-08               South East     18
## 1614  2020-11-09               South East     19
## 1615  2020-11-10               South East     20
## 1616  2020-11-11               South East     19
## 1617  2020-11-12               South East     20
## 1618  2020-11-13               South East     12
## 1619  2020-11-14               South East     24
## 1620  2020-11-15               South East     24
## 1621  2020-11-16               South East     22
## 1622  2020-11-17               South East     23
## 1623  2020-11-18               South East     25
## 1624  2020-11-19               South East     21
## 1625  2020-11-20               South East     17
## 1626  2020-11-21               South East     19
## 1627  2020-11-22               South East     29
## 1628  2020-11-23               South East     25
## 1629  2020-11-24               South East     21
## 1630  2020-11-25               South East     33
## 1631  2020-11-26               South East     21
## 1632  2020-11-27               South East      6
## 1633  2020-03-01               South West      0
## 1634  2020-03-02               South West      0
## 1635  2020-03-03               South West      0
## 1636  2020-03-04               South West      0
## 1637  2020-03-05               South West      0
## 1638  2020-03-06               South West      0
## 1639  2020-03-07               South West      0
## 1640  2020-03-08               South West      0
## 1641  2020-03-09               South West      0
## 1642  2020-03-10               South West      0
## 1643  2020-03-11               South West      1
## 1644  2020-03-12               South West      0
## 1645  2020-03-13               South West      0
## 1646  2020-03-14               South West      1
## 1647  2020-03-15               South West      0
## 1648  2020-03-16               South West      0
## 1649  2020-03-17               South West      2
## 1650  2020-03-18               South West      2
## 1651  2020-03-19               South West      4
## 1652  2020-03-20               South West      3
## 1653  2020-03-21               South West      6
## 1654  2020-03-22               South West      7
## 1655  2020-03-23               South West      8
## 1656  2020-03-24               South West      7
## 1657  2020-03-25               South West      9
## 1658  2020-03-26               South West     11
## 1659  2020-03-27               South West     13
## 1660  2020-03-28               South West     21
## 1661  2020-03-29               South West     18
## 1662  2020-03-30               South West     23
## 1663  2020-03-31               South West     23
## 1664  2020-04-01               South West     21
## 1665  2020-04-02               South West     23
## 1666  2020-04-03               South West     30
## 1667  2020-04-04               South West     42
## 1668  2020-04-05               South West     32
## 1669  2020-04-06               South West     34
## 1670  2020-04-07               South West     39
## 1671  2020-04-08               South West     47
## 1672  2020-04-09               South West     24
## 1673  2020-04-10               South West     46
## 1674  2020-04-11               South West     43
## 1675  2020-04-12               South West     23
## 1676  2020-04-13               South West     27
## 1677  2020-04-14               South West     24
## 1678  2020-04-15               South West     32
## 1679  2020-04-16               South West     29
## 1680  2020-04-17               South West     33
## 1681  2020-04-18               South West     25
## 1682  2020-04-19               South West     31
## 1683  2020-04-20               South West     26
## 1684  2020-04-21               South West     26
## 1685  2020-04-22               South West     23
## 1686  2020-04-23               South West     17
## 1687  2020-04-24               South West     19
## 1688  2020-04-25               South West     15
## 1689  2020-04-26               South West     27
## 1690  2020-04-27               South West     13
## 1691  2020-04-28               South West     17
## 1692  2020-04-29               South West     15
## 1693  2020-04-30               South West     26
## 1694  2020-05-01               South West      6
## 1695  2020-05-02               South West      7
## 1696  2020-05-03               South West     10
## 1697  2020-05-04               South West     17
## 1698  2020-05-05               South West     14
## 1699  2020-05-06               South West     19
## 1700  2020-05-07               South West     16
## 1701  2020-05-08               South West      6
## 1702  2020-05-09               South West     11
## 1703  2020-05-10               South West      5
## 1704  2020-05-11               South West      8
## 1705  2020-05-12               South West      7
## 1706  2020-05-13               South West      7
## 1707  2020-05-14               South West      6
## 1708  2020-05-15               South West      4
## 1709  2020-05-16               South West      4
## 1710  2020-05-17               South West      6
## 1711  2020-05-18               South West      4
## 1712  2020-05-19               South West      6
## 1713  2020-05-20               South West      1
## 1714  2020-05-21               South West      9
## 1715  2020-05-22               South West      7
## 1716  2020-05-23               South West      6
## 1717  2020-05-24               South West      3
## 1718  2020-05-25               South West      8
## 1719  2020-05-26               South West     11
## 1720  2020-05-27               South West      5
## 1721  2020-05-28               South West     10
## 1722  2020-05-29               South West      7
## 1723  2020-05-30               South West      3
## 1724  2020-05-31               South West      2
## 1725  2020-06-01               South West      7
## 1726  2020-06-02               South West      2
## 1727  2020-06-03               South West      7
## 1728  2020-06-04               South West      2
## 1729  2020-06-05               South West      2
## 1730  2020-06-06               South West      1
## 1731  2020-06-07               South West      3
## 1732  2020-06-08               South West      3
## 1733  2020-06-09               South West      0
## 1734  2020-06-10               South West      1
## 1735  2020-06-11               South West      2
## 1736  2020-06-12               South West      2
## 1737  2020-06-13               South West      2
## 1738  2020-06-14               South West      0
## 1739  2020-06-15               South West      2
## 1740  2020-06-16               South West      2
## 1741  2020-06-17               South West      0
## 1742  2020-06-18               South West      0
## 1743  2020-06-19               South West      0
## 1744  2020-06-20               South West      2
## 1745  2020-06-21               South West      0
## 1746  2020-06-22               South West      1
## 1747  2020-06-23               South West      1
## 1748  2020-06-24               South West      1
## 1749  2020-06-25               South West      0
## 1750  2020-06-26               South West      3
## 1751  2020-06-27               South West      0
## 1752  2020-06-28               South West      0
## 1753  2020-06-29               South West      1
## 1754  2020-06-30               South West      0
## 1755  2020-07-01               South West      0
## 1756  2020-07-02               South West      0
## 1757  2020-07-03               South West      0
## 1758  2020-07-04               South West      0
## 1759  2020-07-05               South West      1
## 1760  2020-07-06               South West      0
## 1761  2020-07-07               South West      0
## 1762  2020-07-08               South West      2
## 1763  2020-07-09               South West      0
## 1764  2020-07-10               South West      1
## 1765  2020-07-11               South West      0
## 1766  2020-07-12               South West      0
## 1767  2020-07-13               South West      1
## 1768  2020-07-14               South West      0
## 1769  2020-07-15               South West      0
## 1770  2020-07-16               South West      0
## 1771  2020-07-17               South West      1
## 1772  2020-07-18               South West      0
## 1773  2020-07-19               South West      0
## 1774  2020-07-20               South West      0
## 1775  2020-07-21               South West      0
## 1776  2020-07-22               South West      0
## 1777  2020-07-23               South West      0
## 1778  2020-07-24               South West      0
## 1779  2020-07-25               South West      0
## 1780  2020-07-26               South West      0
## 1781  2020-07-27               South West      0
## 1782  2020-07-28               South West      0
## 1783  2020-07-29               South West      0
## 1784  2020-07-30               South West      1
## 1785  2020-07-31               South West      0
## 1786  2020-08-01               South West      0
## 1787  2020-08-02               South West      0
## 1788  2020-08-03               South West      0
## 1789  2020-08-04               South West      0
## 1790  2020-08-05               South West      0
## 1791  2020-08-06               South West      0
## 1792  2020-08-07               South West      0
## 1793  2020-08-08               South West      0
## 1794  2020-08-09               South West      0
## 1795  2020-08-10               South West      0
## 1796  2020-08-11               South West      0
## 1797  2020-08-12               South West      0
## 1798  2020-08-13               South West      0
## 1799  2020-08-14               South West      1
## 1800  2020-08-15               South West      0
## 1801  2020-08-16               South West      0
## 1802  2020-08-17               South West      2
## 1803  2020-08-18               South West      0
## 1804  2020-08-19               South West      0
## 1805  2020-08-20               South West      0
## 1806  2020-08-21               South West      0
## 1807  2020-08-22               South West      0
## 1808  2020-08-23               South West      0
## 1809  2020-08-24               South West      0
## 1810  2020-08-25               South West      1
## 1811  2020-08-26               South West      0
## 1812  2020-08-27               South West      1
## 1813  2020-08-28               South West      0
## 1814  2020-08-29               South West      0
## 1815  2020-08-30               South West      0
## 1816  2020-08-31               South West      0
## 1817  2020-09-01               South West      0
## 1818  2020-09-02               South West      0
## 1819  2020-09-03               South West      0
## 1820  2020-09-04               South West      0
## 1821  2020-09-05               South West      0
## 1822  2020-09-06               South West      0
## 1823  2020-09-07               South West      0
## 1824  2020-09-08               South West      1
## 1825  2020-09-09               South West      0
## 1826  2020-09-10               South West      0
## 1827  2020-09-11               South West      0
## 1828  2020-09-12               South West      0
## 1829  2020-09-13               South West      1
## 1830  2020-09-14               South West      0
## 1831  2020-09-15               South West      0
## 1832  2020-09-16               South West      0
## 1833  2020-09-17               South West      1
## 1834  2020-09-18               South West      0
## 1835  2020-09-19               South West      0
## 1836  2020-09-20               South West      1
## 1837  2020-09-21               South West      0
## 1838  2020-09-22               South West      0
## 1839  2020-09-23               South West      0
## 1840  2020-09-24               South West      1
## 1841  2020-09-25               South West      0
## 1842  2020-09-26               South West      0
## 1843  2020-09-27               South West      0
## 1844  2020-09-28               South West      0
## 1845  2020-09-29               South West      0
## 1846  2020-09-30               South West      0
## 1847  2020-10-01               South West      0
## 1848  2020-10-02               South West      1
## 1849  2020-10-03               South West      0
## 1850  2020-10-04               South West      0
## 1851  2020-10-05               South West      0
## 1852  2020-10-06               South West      1
## 1853  2020-10-07               South West      0
## 1854  2020-10-08               South West      1
## 1855  2020-10-09               South West      1
## 1856  2020-10-10               South West      0
## 1857  2020-10-11               South West      4
## 1858  2020-10-12               South West      2
## 1859  2020-10-13               South West      0
## 1860  2020-10-14               South West      3
## 1861  2020-10-15               South West      1
## 1862  2020-10-16               South West      2
## 1863  2020-10-17               South West      8
## 1864  2020-10-18               South West      2
## 1865  2020-10-19               South West      2
## 1866  2020-10-20               South West      3
## 1867  2020-10-21               South West      6
## 1868  2020-10-22               South West      6
## 1869  2020-10-23               South West      5
## 1870  2020-10-24               South West      5
## 1871  2020-10-25               South West      5
## 1872  2020-10-26               South West      7
## 1873  2020-10-27               South West      6
## 1874  2020-10-28               South West      8
## 1875  2020-10-29               South West     11
## 1876  2020-10-30               South West      8
## 1877  2020-10-31               South West      4
## 1878  2020-11-01               South West      5
## 1879  2020-11-02               South West     11
## 1880  2020-11-03               South West      6
## 1881  2020-11-04               South West      8
## 1882  2020-11-05               South West      5
## 1883  2020-11-06               South West     11
## 1884  2020-11-07               South West      9
## 1885  2020-11-08               South West     10
## 1886  2020-11-09               South West     11
## 1887  2020-11-10               South West      6
## 1888  2020-11-11               South West     13
## 1889  2020-11-12               South West     16
## 1890  2020-11-13               South West      9
## 1891  2020-11-14               South West      8
## 1892  2020-11-15               South West     15
## 1893  2020-11-16               South West     16
## 1894  2020-11-17               South West     14
## 1895  2020-11-18               South West     24
## 1896  2020-11-19               South West     14
## 1897  2020-11-20               South West     21
## 1898  2020-11-21               South West     22
## 1899  2020-11-22               South West     21
## 1900  2020-11-23               South West     13
## 1901  2020-11-24               South West     16
## 1902  2020-11-25               South West     18
## 1903  2020-11-26               South West     11
## 1904  2020-11-27               South West      6

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-11-26"

The completion date of the NHS Pathways data is Thursday 26 Nov 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 20 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 20 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -23.274   -8.402   -3.979    4.755   17.352  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.088e+00  7.228e-02   56.55   <2e-16 ***
## note_lag    1.965e-05  8.348e-07   23.54   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 64.89657)
## 
##     Null deviance: 40839  on 213  degrees of freedom
## Residual deviance: 13840  on 212  degrees of freedom
##   (20 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##    59.59966     1.00002
exp(confint(lag_mod))
##                 2.5 %    97.5 %
## (Intercept) 51.576860 68.479305
## note_lag     1.000018  1.000021

Rsq(lag_mod)
## [1] 0.6610968

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                              sysname 
##                                                                                             "Darwin" 
##                                                                                              release 
##                                                                                             "19.6.0" 
##                                                                                              version 
## "Darwin Kernel Version 19.6.0: Thu Oct 29 22:56:45 PDT 2020; root:xnu-6153.141.2.2~1/RELEASE_X86_64" 
##                                                                                             nodename 
##                                                                            "Mac-1606642446242.local" 
##                                                                                              machine 
##                                                                                             "x86_64" 
##                                                                                                login 
##                                                                                               "root" 
##                                                                                                 user 
##                                                                                             "runner" 
##                                                                                       effective_user 
##                                                                                             "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.3                         
## year           2020                        
## month          10                          
## day            10                          
## svn rev        79318                       
## language       R                           
## version.string R version 4.0.3 (2020-10-10)
## nickname       Bunny-Wunnies Freak Out

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.3     ggpubr_0.4.0         lubridate_1.7.9.2   
##  [4] chngpt_2020.10-12    cyphr_1.1.0          DT_0.16             
##  [7] kableExtra_1.3.1     janitor_2.0.1        remotes_2.2.0       
## [10] projections_0.5.1    earlyR_0.0.5         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.3      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.2          purrr_0.3.4          readr_1.4.0         
## [25] tidyr_1.1.2          tibble_3.0.4         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_1.0.0           reportfactory_0.0.6 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_2.0-0  selectr_0.4-2     ggsignif_0.6.0   
##  [5] ellipsis_0.3.1    rprojroot_2.0.2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.13   farver_2.0.3      fansi_0.4.1       splines_4.0.3    
## [13] knitr_1.30        jsonlite_1.7.1    nloptr_1.2.2.2    broom_0.7.2      
## [17] dbplyr_2.0.0      compiler_4.0.3    httr_1.4.2        backports_1.2.0  
## [21] assertthat_0.2.1  Matrix_1.2-18     cli_2.2.0         htmltools_0.5.0  
## [25] tools_4.0.3       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.5       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.5       nlme_3.1-149     
## [33] matchmaker_0.1.1  crosstalk_1.1.0.1 xfun_0.19         ps_1.4.0         
## [37] openxlsx_4.2.3    lme4_1.1-25       lifecycle_0.2.0   statmod_1.4.35   
## [41] rstatix_0.6.0     MASS_7.3-53       scales_1.1.1      hms_0.5.3        
## [45] parallel_4.0.3    sodium_1.1        yaml_2.2.1        curl_4.3         
## [49] gridExtra_2.3     stringi_1.5.3     kyotil_2020.10-12 boot_1.3-25      
## [53] zip_2.1.1         rlang_0.4.9       pkgconfig_2.0.3   evaluate_0.14    
## [57] lattice_0.20-41   labeling_0.4.2    htmlwidgets_1.5.2 cowplot_1.1.0    
## [61] tidyselect_1.1.0  plyr_1.8.6        magrittr_2.0.1    R6_2.5.0         
## [65] generics_0.1.0    DBI_1.1.0         pillar_1.4.7      haven_2.3.1      
## [69] foreign_0.8-80    withr_2.3.0       mgcv_1.8-33       survival_3.2-7   
## [73] abind_1.4-5       modelr_0.1.8      crayon_1.3.4      car_3.0-10       
## [77] utf8_1.1.4        rmarkdown_2.5     viridis_0.5.1     grid_4.0.3       
## [81] readxl_1.3.1      data.table_1.13.2 reprex_0.3.0      digest_0.6.27    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0